The VLA-COSMOS 3 GHz Large Project: Continuum data ...vs/papers_dr1/Smolcic_et_al_data.pdf3 NAF-Osservatorio Astronomico di Bologna, Via Ranzani 1, I - 40127 Bologna, Italy 4 California

Astronomy & Astrophysics manuscript no. ms_2c c©ESO 2016June 20, 2016

The VLA-COSMOS 3 GHz Large Project: Continuum data and

source catalog release

V. Smolcic1, M. Novak1, M. Bondi2, P. Ciliegi3, K. P. Mooley4, E. Schinnerer5, G. Zamorani3, F. Navarette6,S. Bourke4, A. Karim6, E. Vardoulaki6 , S. Leslie5, J. Delhaize1, C. L. Carilli7, S. T. Myers7, N. Baran1, I. Delvecchio1,

O. Miettinen1, J. Banfield8, 9, M. Balokovic4, F. Bertoldi6, P. Capak10, D. A. Frail7, G. Hallinan4, H. Hao11,N. Herrera Ruiz12, A. Horesh13, O. Ilbert14, H. Intema7, V. Jelic15, 16, 17, H-R. Klöckner18, 19, J. Krpan1, S. R. Kulkarni4,

H. McCracken20, C. Laigle19, E. Middleberg12 , E. Murphy21, M. Sargent22, N. Z. Scoville4, K. Sheth21

1 Department of Physics, University of Zagreb, Bijenicka cesta 32, 10002 Zagreb, Croatia2 Istituto di Radioastronomia di Bologna - INAF, via P. Gobetti, 101, 40129, Bologna, Italy3 NAF-Osservatorio Astronomico di Bologna, Via Ranzani 1, I - 40127 Bologna, Italy4 California Institute of Technology, MC 249-17, 1200 East California Boulevard, Pasadena, CA 911255 Max-Planck-Institut fur Astronomie, Konigstuhl 17, D-69117 Heidelberg, Germany6 Argelander Institut for Astronomy, Auf dem Hügel 71, Bonn, 53121, Germany7 National Radio Astronomy Observatory, P.O. Box 0, Socorro, NM 87801, USA8 CSIRO Australia Telescope National Facility, PO Box 76, Epping, NSW 1710, Australia9 Research School of Astronomy and Astrophysics, Australian National University, Weston Creek, ACT 2611, Australia

10 Spitzer Science Center, 314-6 Caltech, Pasadena, CA 91125, USA11 Smithsonian Astrophysical Observatory, 60 Garden St, Cambridge, MA 02138, USA12 Astronomisches Institut, Ruhr-Universität Bochum, Universitätsstr. 150, 44801, Bochum, Germany13 Benoziyo Center for Astrophysics, Weizmann Institute of Science, 76100 Rehovot, Israel14 Aix Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille), UMR 7326, 13388, Marseille, France15 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV, Groningen, The Netherlands16 ASTRON - The Netherlands Institute for Radio Astronomy, PO Box 2, 7990 AA, Dwingeloo, The Netherlands17 Ruder Boškovic Institute, Bijenicka cesta 54, 10000 Zagreb, Croatia18 Subdepartment of Astrophysics, University of Oxford, Denys-Wilkinson Building, Keble Road, Oxford OX1 3RH, UK19 Max-Planck-Institut f ur Radioastronomie, Auf dem H:ugel 69, D-53121 Bonn, Germany20 Institut d’Astrophysique de Paris, UMR7095 CNRS, Universit e Pierre et Marie Curie, 98 bis Boulevard Arago, 75014, Paris,

France21 National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA22 Astronomy Centre, Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH, UK

Received ; accepted

ABSTRACT

We present the VLA-COSMOS 3 GHz Large Project based on 384 hours of observations with the Karl G. Jansky Very Large Array(VLA) at 3 GHz (10 cm) toward the 2 square degree COSMOS field. The final mosaic reaches a median rms of 2.3 µJy beam−1 overthe 2 square degrees, at an angular resolution of 0.75′′ . To fully account for the spectral shape and resolution variations across thebroad (2 GHz) band we image all data with a multi-scale, multi-frequency synthesis algorithm. We present a catalog of 10,830 radiosources down to 5σ, out of which 67 are combined from multiple components. Comparing the positions of our 3 GHz sources withthose from the VLBA-COSMOS survey, we estimate that the astrometry is accurate to 0.01′′ at the bright end (signal-to-noise ratio,SNR3GHz > 20). Survival analysis on our data combined with the VLA-COSMOS 1.4 GHz Joint Project catalog yields an expectedmedian radio spectral index of α = −0.7. We compute completeness corrections via Monte Carlo simulations to derive the corrected3 GHz source counts. Our counts are in agreement with previously derived 3 GHz counts based on single-pointing (0.087 squaredegrees) VLA data. In summary, the VLA-COSMOS 3 GHz Large Project provides to-date simultaneously the largest and deepestradio continuum survey at high (0.75′′) angular resolution, bridging the gap between last-generation and next-generation surveys.

Key words. galaxies: fundamental parameters – galaxies: active, evolution – cosmology: observations – radio continuum: galaxies

1. Introduction

One of the main quests in modern cosmology is understand-ing the formation of galaxies, and their evolution through cos-mic time. In the past decade it has been demonstrated that apanchromatic, X-ray to radio, observational approach is key todevelop a consensus on galaxy formation and evolution (e.g.,Dickinson et al. 2003; Scoville et al. 2007; Driver et al. 2009,

2011; Koekemoer et al. 2011; Grogin et al. 2011). In this con-text, the radio regime offers an indispensable window towardstar formation and supermassive black hole properties of galax-ies as radio continuum emission i) provides a dust-unbiased starformation tracer at high angular resolution (e.g., Condon 1992;Haarsma et al. 2000; Seymour et al. 2008; Smolcic et al. 2009b;Karim et al. 2011), and ii) directly probes those active galac-tic nuclei (AGN) that are hosted by the most massive quiescent

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galaxies and deemed crucial for massive galaxy formation (e.g.,Croton et al. 2006; Bower et al. 2006; Best et al. 2006; Evanset al. 2006; Hardcastle et al. 2007; Smolcic et al. 2009a; Smolcic2009; Smolcic & Riechers 2011; Smolcic et al. 2015).

In the past decades radio interferometers, such as theVery Large Array (VLA), Australia Telescope Compact Array(ATCA), and Giant Meterwave Radio Telescope (GMRT), sur-veyed fields with different sizes (ranging from tens of square ar-cminutes to thousands of square degrees), depths (microjanskyto Jansky), as well as multi-wavelength coverage (e.g., Beckeret al. 1995; Condon et al. 1998; Ciliegi et al. 1999; Georgakakiset al. 1999; Bock et al. 1999; Prandoni et al. 2001; Condon et al.2003; Hopkins et al. 2003; Schinnerer et al. 2004; Bondi et al.2003, 2007; Norris et al. 2005; Schinnerer et al. 2007, 2010;Afonso et al. 2005; Tasse et al. 2007; Smolcic et al. 2008a; Owen& Morrison 2008; Miller et al. 2008, 2013; Owen et al. 2009;Condon et al. 2012; Smolcic et al. 2014; Hales et al. 2014).These past surveys have shown that deep observations at highangular resolution (. 1′′) with exquisite panchromatic cover-age are critical to comprehensively study the radio propertiesof the main galaxy populations, avoiding cosmic variance withlarge area coverage (e.g., Padovani et al. 2009; Padovani 2011;Smolcic et al. 2008a, 2009b,a; Smolcic 2009; Smolcic & Riech-ers 2011; Seymour et al. 2008; Bonzini et al. 2012, 2013). Inthis context, large area surveys down to unprecedented depthsare planned with new and upgraded facilities (e.g., VLA, West-erbork, ASKAP, MeerKAT, SKA; e.g., Jarvis 2012; Norris et al.2011, 2013, 2015; Prandoni & Seymour 2015). This is illustratedin Fig. 1, where for various (past, current and future) radio con-tinuum surveys the survey’s 1σ sensitivity as a function of areacovered is shown. The VLA-COSMOS 3 GHz Large Projectbridges the gap between past and future radio continuum sur-veys by covering an area as large as 2 square degrees down to asensitivity reached to-date only for single pointing observations.This allows for individual detections of > 10, 000 radio sources,further building on the already extensive radio coverage of theCOSMOS field at 1.4 GHz VLA (VLA-COSMOS Large, Deepand Joint projects; Schinnerer et al. 2004, 2007, 2010), 320 MHzVLA (Smolcic et al., 2014), 325 MHz and 616 MHz GMRT data(Karim et al., in prep.; Brady et al., in prep.), 6 GHz VLA (My-ers et al., in prep.), as well as the deep multi-wavelength X-rayto mm photometry (Scoville et al. 2007; Koekemoer et al. 2007;Hasinger et al. 2007; Capak et al. 2007; Sanders et al. 2007;Bertoldi et al. 2007; Elvis et al. 2009; Ilbert et al. 2013; Mc-Cracken et al. 2012; Scott et al. 2008; Aretxaga et al. 2011;Smolcic et al. 2012; Miettinen et al. 2015; Civano et al. 2016;Laigle et al. 2016, Capak et al., in prep.) and more than 97,000optical spectroscopic redshifts (Salvato et al., in prep.; zCOS-MOS, Lilly et al. 2007, 2009; Trump et al. 2007; Prescott et al.2006; Le Fèvre et al. 2015; Aihara et al. 2011; Nagao et al., priv.comm.). This further makes the survey part of one of the richestmulti-wavelength data-sets available to-date.

Radio continuum surveys at 3 GHz with the upgraded VLAare still sparse in the literature. Condon et al. (2012) performedsingle-pointing observations targeting the Lockman hole for 50-hours on-source with the VLA in C-configuration. The obser-vations resulted in a confusion-limited map with an rms of1 µJy beam−1. Based on this they constrained the counts of dis-crete sources in the 1 − 10 µJy range via a P(D) analysis. Amore complex P(D) analysis using the same data was applied byVernstrom et al. (2014) who probed the counts down to 0.1 µJy.Both results are qualitatively in agreement with the already well-known flattening of the radio source counts (normalized to theN(S ) ∝ S −3/2 of a static Euclidian space) below flux densities

Fig. 1. Sensitivity (at the observed frequency of the given survey) vs.area for past, current, and future radio continuum surveys.

of S 1.4GHz ≈ 1 mJy, and a further decrease of the counts withdecreasing flux density below S 1.4GHz ≈ 60 µJy. Such a shapeof radio source counts is expected due to the cosmic evolutionof galaxy populations (e.g., Hopkins et al. 2000; Wilman et al.2008; Béthermin et al. 2012), but contrary to that obtained basedon i) the previous Lockman hole observations at 1.4 GHz (Owen& Morrison, 2008), and ii) a comparison of the sky brightnesstemperature measured by the ARCADE 2 experiment (Fixsenet al., 2009) with that derived from the integral of the observedradio source counts (Vernstrom et al., 2011). The latter resultsinstead point to a rise of the counts with decreasing flux densityat these levels. To investigate this further, we here derive the ra-dio source counts using our VLA-COSMOS 3GHz Large projectdata, yielding the deepest radio counts derived to-date based ondirect source detections.

In Sect. 2 we describe the VLA 3 GHz observations, calibra-tion and imaging. We present the catalog extraction in Sect. 3,an analysis of the radio spectral indices in Sect. 4 , the radiosource count corrections in Sect. 5 and the radio source countsin Sect. 6. We summarize our products and results in Sect. 7. Wedefine the radio spectral index α as S ν ∝ ν

α, where S ν is fluxdensity at frequency ν.

2. Observations and data reduction

2.1. Observations

A total of 384 hours of observations toward the COSMOS fieldwere taken in S-band using the S 3s full width set-up covering abandwidth of 2048 MHz centered at 3 GHz, and separated intosixteen 128 MHz-wide spectral windows (SPWs hereafter), withfull polarization, and a 3s signal-averaging time. The observa-tions were taken from November 2012 to January 2013, Juneto August 2013 and February to May 2013 in A- (324 hours)and C-configurations (60 hours; Legacy ID AS1163). Sixty-fourpointings, separated by 10′ in Right Ascension and Declination,


Smolcic et al.: VLA-COSMOS 3 GHz Large Project

Fig. 2. Pointing pattern used for the 3 GHz VLA-COSMOS LargeProject. The centers of the 192 pointings are marked by the plus signs.Circles indicate the primary beam of each pointing, represented here bythe HPBW at 3 GHz (15′; note that the primary beam HPBW is a func-tion of frequency and varies by a factor 2 between the lower and upperedge of the S-band).

corresponding to 2/3 of the half-power beam width (HPBW) atthe central frequency of 3 GHz, were chosen to cover the full 2square degree COSMOS field. To achieve a uniform rms overthe field three sets of 64 pointings (the first set is nominal, thesecond one is shifted by 5′ in Right Ascension and Declina-tion, while the third set is shifted by −5′ in Right Ascension)in such a grid were used, resulting in a total of 192 pointings,shown in Fig. 2. Observing runs of 5 and 3 hours length wereconducted. In each observing run J1331+3030 was observed forflux and bandpass calibration for about 3-5 minutes on-source(J0521+166 was used only for the first day of observations) atthe end of every run, J1024-0052 was observed every 30 min-utes for 1m40s on-source for gain and phase calibration, whilethe source J0713+4349 was observed for 5 minutes on-sourceat the beginning of each run for polarization leakage calibration.During the five hour observing runs each pointing was visitedtwice, while the order of the pointing coverage blocks duringthe fixed 5-hour observing blocks was changed between the dif-ferent observing runs to optimize the uv-coverage. During the3-hour observing blocks each pointing was visited once, and agood uv-coverage was assured via dynamic scheduling. Typi-cally, 26 antennas were used during each observing run. The A-configuration observations were mostly conducted under good toexcellent weather conditions. C-configuration observations werepartially affected by poor weather conditions (Summer thunder-storms) yielding on some days up to 30% higher rms than ex-pected based on the VLA exposure calculator.

2.2. Calibration

Calibration of the data was performed via the AIPSLite data re-duction pipeline (Bourke et al., 2014) developed for the Caltech-NRAO Stripe 82 Survey (Mooley et al., 2016). This pipelinewas adapted for the VLA-COSMOS 3 GHz Large Project (as

described below) and it follows, in general, the procedures out-lined in Chapter E of the AIPS Cookbook1.

In brief, the data is first loaded with the Obit2 task BDFIn.Band edges, and to a larger extent IF edges, were then flaggedwith the task UVFLG. SPWs 2 and 3, found to be irreparably cor-rupted by radio frequency interference (RFI) in all observations(see Fig. 3), were entirely flagged using the task UVFLG. Afterflagging, FRING, BPASS, SETJY, CALIB, GETJY, and CLCALwereused to derive the delay, bandpass, and complex gain solutions.Polarization calibration was performed using the tasks RLDLY,PCAL, and RLDIF as detailed in Sect. 7 of Chapter E in the AIPSCookbook. The task RFLAG was used to flag all target pointingsand the flags were applied using the UVCOP task. The derivedcalibration was applied and the calibrated dataset was producedwith the SPLAT task. Finally, the calibrated UV data was savedto disk using the task FITTP. During the pipeline process sev-eral diagnostic plots were generated to assess the quality of thecalibration: bandpass solutions, antenna gains as a function oftime, calibrated spectrum of the gain calibrator, and calibratedamplitude versus phase plots of the gain calibrator per pointing.In Table 1 we list the statistics for the amplitude of the phasecalibrator in each SPW for all observing blocks. The averageamplitude scatter around the mean is typically 2 − 3% (with theexception of the highest frequency SPWs, for which it is higherthan 10% 3). The combined typical scatter around the mean is∼ 5%. This assures a good flux calibration. Through our testswe find that, in the majority of observations, RFI adversely af-fects the system temperature measurements, and hence we haveleft out the TSYS correction from the calibration process.

At this point the pipeline diverges in two directions to:i) image the target fields, and ii) produce and export a cali-brated dataset in preparation for mosaicing. To image the tar-get fields they were split out with calibration applied (using thetask SPLIT). The fields were then further auto-flagged (usingthe task RFLAG), imaged (using the task IMAGR), and exported(using the task FITTP) in parallel. The calibrated dataset wasgenerated by applying RFLAG and imaging the target fields, in-cluding applying flags (using the task UVCOP), calibration (usingthe task SPLAT), and exporting the uv-data and maps (using thetask FITTP).

The pipeline performance and output were tested by i) man-ually reducing separate blocks of VLA-COSMOS observationsand comparing the results with the pipeline output, and ii) com-paring the output to the CASA4-based NRAO reduction pipeline

1 http://www.aips.nrao.edu/cook.html2 http://www.cv.nrao.edu/˜bcotton/Obit.html3 We note that the SPWs marked 14, 15, and 16 have low ampli-tude RFI in the LL polarization, and the phases are significantlyaffected for some observations. The C-configuration data at the up-per end of the S-band are mostly unusable due to this RFI. Thesedata have been manually flagged, and we additionally ran RFLAGon the rest of the C-configuration data to further remove bad dataand extend flags in frequency and in time. The A-configuration datafor these SPWs is generally good. Our imaging tests show that thedata from these SPWs generally improves the sensitivity, but lim-its the dynamic range for certain pointings. Looking at the overallimaging performance, we have decided to retain these SPWs. Notethat, despite the "data drop-outs", the median flux density values ofthe phase calibrator (J1024-0052; Table 1) are consistent with thespectral parameters inferred from the other SPWs.4 Common Astronomy Software Applications; CASA is developed byan international consortium of scientists based at the NRAO, the Euro-pean Southern Observatory (ESO), the National Astronomical Obser-vatory of Japan (NAOJ), the CSIRO Australia Telescope National Fa-cility (CSIRO/ATNF), and the Netherlands Institute for Radio Astron-



Fig. 3. Raw spectra of the gain calibrator source, i.e. phase vs. channel, (top frame in each of the four panels) and amplitude vs. channel (bottomframe in each of the four panels) for the RR and LL polarizations (top panels and bottom panels respectively). The panels to the left are for onenight of observation in the A array configuration and the panels to the right are for a C array observation. No calibration was applied. All baselinesand all pointings of the gain calibrator source have been combined to produce these plots. Note the RFI in sub-bands 2 and 3.

Table 1. Amplitude of the phase calibrator (J1024-0052) in each SPWfor all observing blocks

SPW Frequency Mean flux Median flux Standard(GHz) density (Jy) density (Jy) deviation (Jy)

1 2.060 0.739 0.735 0.0294 2.444 0.707 0.704 0.0255 2.572 0.700 0.696 0.0236 2.700 0.684 0.680 0.0237 2.828 0.668 0.665 0.0248 2.956 0.652 0.648 0.0269 3.084 0.645 0.642 0.02010 3.212 0.635 0.632 0.02011 3.340 0.625 0.622 0.02112 3.468 0.615 0.611 0.02013 3.596 0.603 0.600 0.02114 3.724 0.539 0.579 0.12915 3.852 0.525 0.569 0.15316 3.980 0.535 0.566 0.124

for randomly selected data taken in the A- and C-array configu-rations. No obvious differences were found. As the pipeline usedhere was tailored specifically to the COSMOS field (e.g., it in-cludes polarization calibration), after this verification it was fur-ther applied to the remaining VLA-COSMOS datasets.

The calibrated uv-datasets output by the pipeline for eachobserving block were first run through the AIPS task UVFIXto assure accurately computed positions. We note that applyingUVFIX at the end of calibration has the same effect as applying itat the beginning of calibration. They were then further processedin CASA by clipping each calibrated uv-dataset in amplitude(above 0.4 Jy) using the task FLAGDATA5, splitting the individualpointings using the task SPLIT, and concatenating all existingobservations of the same pointing using the task CONCAT. Theconcatenated (u, v) data for each pointing were then imagedprior to being combined into the final mosaic as described indetail in the next section.

omy (ASTRON) under the guidance of NRAO. See http://casa.nrao.edu;(McMullin et al., 2007)5 In total, about 30-35% of the data were flagged (using the tasksRFLAG and FLAGDATA).

2.3. Self-calibration, imaging and mosaicing

To image our data we used the multi-scale multi-frequency syn-thesis (MSMF) algorithm developed by Rau & Cornwell (2011)and implemented in CASA. This method uses the entire 2 GHzbandwidth at once to calculate the monochromatic flux densityat 3 GHz and a spectral index between 2 and 4 GHz. After exten-sive testing of various imaging methods (see, e.g., Novak et al.2015) we settled for the MSMF method as it allows for a com-bination of the best possible resolution, rms, and image quality.Due to the large data volume, joint deconvolution was not practi-cal and we imaged each pointing individually and then combinedthem into a mosaic in the image plane.

In 44 out of 192 pointings we found sources that were brightenough (peak surface brightness higher than 5 mJy beam−1) toallow for self-calibration. To prevent artifacts affecting the modelused for self-calibration small clean masks were centered aroundbright sources. An integration time of 3 min, which roughly cor-responds to one scan length, was used to obtain phase-gain so-lutions for these pointings (i.e. only the phase part of the com-plex gain was solved for and applied). Self-calibration typi-cally could not find a solution for 10% of the data with the frac-tion increasing to 20% for a few pointings which was the max-imum value we allowed. We applied gain solutions to the uv-data but did not apply the flags calculated in the self-calibrationprocess as that usually increased the noise in the map. For theremaining pointings we applied phase-gains obtained by self-calibrating the phase-calibrator J1024-0052 as it further reducedartifacts and sidelobes around brighter sources as illustrated inFig. 4.

We used the CLEAN task with Briggs weighting scheme forgridding of visibilities with a robust parameter of 0.5 to obtainthe best compromise between the resolution and the noise. TwoTaylor terms (nterms=2: TT0 and TT1) were used for multi-frequency synthesis, which allows the reconstruction of the totalintensities and spectral slopes (Rau & Cornwell, 2011). Eachpointing was tapered with its own Gaussian to achieve acircular beam with the difference between the major andthe minor axis being 3% at maximum (see Fig. 5). Prior tothis step the beam was slightly elliptical, but the position anglechanged considerably between different pointings. A cyclefactorof 3 was applied for a more robust deconvolution and to pre-vent artifacts in the map possibly caused by sidelobe intersec-tions. Widefield imaging was necessary to produce correct as-



Fig. 4. Artifacts around bright sources before (left panels) and after(right panels) applying self-calibration phase-gain solutions. The rightcolumn panels also have tapering applied that circularizes the beamshape. The top three rows show the same source with a peak surfacebrightness of around S p ≈ 16 mJy beam−1, but located inside threedifferent pointings that were observed during different time epochs.The fourth row shows artifacts around the brightest source in our data(S p ≈ 18 mJy beam−1) which is also extended. The final row illustratesthe improvement when applying self-calibration solutions only from thephase-calibrator as this source with S p ≈ 2 mJy beam−1 has insufficientSNR for self-calibration (see text for details).

trometry far from the pointing center and we used 128 projectionplanes. We cleaned on 3 additional spatial scales correspondingto 2×, 5× and 10× the synthesized beam size to better handleextended sources such as radio jets and lobes. A gain parame-ter of 0.3 was used to speed up this multi-scale algorithm. Eachpointing map was set to 8,000 pixels on-the-side with a pixelsize of 0.2 × 0.2 arcsec2. Cleaning was performed down to 5σin the entire map and further down to 1.5σ using tight masksaround sources. These masks were defined manually across theentire observed field by visually inspecting the mosaic6. Syn-thesized beam size variations between different pointings wereabout 0.03′′, which was small enough to allow restoration of ev-ery cleaned pointing to an average circular beam of 0.75′′. Fi-nally, each pointing was corrected for the frequency-dependentprimary beam response down to a value of 20% (correspondingto a radius of 10.5′) using the WIDEBANDPBCOR task. The noiselevel in the phase-center of an individual pointing was usuallyaround 4-5 µJy beam−1.

To construct the mosaic of all pointings we used our customIDL procedure combined with the AIPS task FLATN to do noiseweighted addition of the individually imaged pointings. Everypixel in the sum was weighted by the inverse square of the local

6 A preliminary mosaic was generated with pointings cleaned down to5σ and then used to define cleaning masks. Masks were usually circleswith 0.7′′ radius, but they were modified where necessary to accommo-date larger (resolved) extended sources. Note that it was not necessaryto set clean boxes around known strong sources outside of the im-aged area.

-0.05 0 0.05 0.1 0.15 0.2

Fig. 5. Left: The final (A+C-configuration combined) dirty beam ofone pointing, after tapering. This beam was used in the cleaning ofthat pointing (see text for details). Right: Mean stack of all 192 dirtybeams. The contribution of radial sidelobes is 10% at maximum.

rms which was determined in the pointing itself via the AIPStask RMSD (see below). We mosaiced both Taylor terms individ-ually using the noise weights calculated from the total intensitymaps. The 3 GHz continuum mosaic is shown in Fig. 6, wherewe overplot Gaussian fits to the pixel surface brightness distribu-tions across the mosaic. Cutouts of several extended sources anda mosaic zoom-in are presented in Fig 7. The visibility functionshowing the covered area at a given rms is presented in Fig. 8.In summary, the final mosaic has a resolution of 0.75′′, with amedian rms of 2.3 µJy beam−1 over the COSMOS 2 square de-grees.

3. Cataloging

3.1. Extracting source components

To extract source components from the VLA-COSMOS MSMFmosaic and catalog their properties we employed blobcat de-veloped by Hales et al. (2012). It uses the flood fill algorithmto find islands of pixels (blobs) above a certain signal-to-noiseratio (SNR) threshold. The local noise map used to evaluate theSNR at each pixel position was created from the total intensitymosaic with the AIPS task RMSDwith a circular mesh size of 100pixels. Once blobcat locates islands, it measures the peak sur-face brightness (S p) by fitting a 2D parabola around the brightestpixel, while the total flux density (S t) is obtained by summing-up the pixel values inside the island and dividing the sum bythe beam size in pixels. In the next step blobcat takes into ac-count a small positive peak surface brightness bias created bythe presence of noise peaks in the map and also corrects for anegative integrated surface brightness bias caused by the finiteisland size used for integration. We used default parameterswhen running blobcat (as Hales et al. 2012 ran extensivesimulations to optimize them; see also Hales et al. 2014), withthe required size of a blob being at least three pixels in RAand 3 pixels in DEC. This was necessary to detect low SNRsources which would have otherwise been missed due to our rel-atively coarse pixel grid. With this setup we recovered 10,899radio source components with local SNR greater or equal to 5across the entire observed area. As detailed in Sect. 3.3 67 com-ponents have been merged into unique, multi-component sourcesresulting in a total of 10,830 radio sources.



Fig. 6. 3 GHz VLA-COSMOS mosaic with overlaid Gaussian fits to the pixel surface brightness distributions in various mosaic sectors. The rmsobtained via the Gaussian fit (in units of µJy beam−1) is indicated in each panel. The panels shown cover the full COSMOS 2 square degree field.We note that the small-scale (∼ 1′) rms variations due to the pointing layout are less than 2%.

3.2. Resolved vs. unresolved sources

In order to determine whether our identified source compo-nents are resolved (i.e. extended, larger than the synthesizedbeam) we make use of the ratio between total flux density (S t)and peak surface brightness (S p) as this is a direct measure ofthe extension of a radio source. The flux densitites were com-puted by blobcat as described in the previous section. Fora perfect Gaussian unresolved source, the peak surface bright-ness in Jy beam−1 equals to the integrated flux density in Jy orS t/S p = 1. The extension of a radio source increases its total fluxdensity when compared to its peak surface brightness, however,background noise can lower it (see Bondi et al. 2003). There-

fore, in Fig. 9 we plot the ratio between the total flux density andthe peak surface brightness as a function of the SNR (=S p/rms)for all 10,899 components in the catalog. To select the resolvedcomponents, we determined the lower envelope of the points inFig. 9, which contains 95% of the components with S t < S p andmirrored it above the S t/S p = 1 line (upper envelope in Fig. 9).The shape of the envelope was chosen following Bondi et al.(2008) and the fit to our data is given as S t/S p = 1+6 ·SNR−1.44.We consider the 3,975 components above the upper envelope asresolved. These resolved components were flagged in the cata-log. For the unresolved components the total flux density was setequal to the peak surface brightness in the catalog.



Fig. 7. Stamps from the VLA-COSMOS 3 GHz continuum mosaicimaged with the MSMF algorithm showing examples of extended andcompact radio sources.

Fig. 8. Visibility plot showing the total area covered down to a givennoise level (black dashed line). Our data extend beyond the COSMOS2 square degree field which ensures more uniform noise inside it (redfull line). The median noise level inside the COSMOS 2 square degreesis σ = 2.3 µJy beam−1.

3.3. Multi-component sources

Large sources with diffuse structures, such as e.g. radio galax-ies (see Fig. 7) or resolved star forming disks, can be listed ina component catalog as multiple entries. This can happen forexample if there is no significant radio emission between thetwo radio lobes, or if the local rms noise is overestimated dueto large scale faint radio emission which affects blobcat abilityto properly detect a contiguous blob. We have identified 10,899components in our mosaic, as described above. In order to gen-

Fig. 9. Ratio of total flux density to peak surface brightness as a func-tion of SNR ratio. Components within the envelopes (gray points) in-dicated by red solid lines are considered unresolved, while those abovethe upper envelope (black points) are considered resolved (see text fordetails).

erate a source catalog, rather than a source component catalogwe aimed at identifying such sources, and converting the mul-tiple entires into one, describing the entire source, i.e. listingits proper total flux density and position. For this purpose wevisually inspected over 2,500 components. The inspected sam-ple was a combination of the i) brightest 2,500 components, ii)all known multi-component sources identified and listed in the1.4 GHz Joint catalog (126 components), and iii) sources withREST > 1 + 30 × SNR−1 (351 components). The REST parameteris a size estimate reported by blobcatwhich can be used to findsources with non-Gaussian morphology, see Hales et al. (2012,2014) for more details. Following the procedure already appliedto the VLA-COSMOS 1.4 GHz survey sources (Schinnerer et al.,2007) these components were visually inspected with respect tothe NIR images, i.e. the z++YJHK stacked maps (Laigle et al.,2016). In total, we identifed 67 multi-component sources. Asfor the previous VLA-COSMOS survey catalogs, we computedtheir total flux densities using the AIPS task TVSTAT withinthe area encompassed by 2σ contours, where σ is the local rmsmeasured as the average rms from a 100-300 pixels wide areasaround the source, ensuring that the rms is not biased by the in-fluence of the strong sources. The source position is then takento be the radio core or optical counterpart position (if identifi-able) or the luminosity weighted mean. In our catalog we thenexcluded all the components combined into the multi-componentsources, and listed instead the multi-component source with theabove defined position and total flux density, setting all othercataloged values to -99. A further column ("multi") was addeddesignating the multi-component sources (multi=1 for a multi-component source, and multi=0 for a single-component source).We note that the number of multi-component sources is smallerthan that identified in the shallower VLA-COSMOS 1.4 GHzsurvey. This is due to the higher frequency of breaking-up largesources into multiple components within the latter as it used theAIPS Search and Destroy source finding algorithm, whencompared to the performance of the blobcat algorithm usedhere. A full assessment of large sources in the survey will bepresented by Vardoulaki et al. (in prep.).



Fig. 10. Astrometry comparison between 3 GHz and 1.4 GHz VLBAdata for 443 VLBA sources (PI: Middelberg, N. Herrera Ruiz et al. inprep.).

3.4. Astrometric accuracy

To assess our astrometric accuracy at the bright end we havecompared the positions of 443 sources at 3 GHz with SNR >20, also detected in the VLBA-COSMOS 1.4 GHz survey (PI:Middelberg; N. Herrera Ruiz et al., in prep.). The results, shownin Fig. 10, yield an excellent agreement with a mean offset of0.01′′ in ∆ RA and 0.00′′ in ∆ DEC and a standard deviationof 0.01′′ for both. We note that we did not correct the cat-alog entries for the 0.01′′ offset in ∆ RA. We took the stan-dard deviation value (0.01′′) as the calibration error in RightAscension and Declination to compute the positional uncer-tainties for our sources using the equations reported in Haleset al. (2012). We note that these are estimated to be accuratefor point-sources, but likely underestimated for resolved sources(see Hales et al. 2012 and references therein for details).

3.5. Bandwidth smearing

Due to the finite bandwidth of the antenna receiver, bandwidthsmearing (BWS) occurs and radially smears peak surface bright-ness while conserving the integrated flux density. The effect is afunction of distance from the phase-center in a given pointingwhile it reaches a constant smearing value in the combined mo-saic (see e.g., Bondi et al. 2008). Although the bandwidth ofthe antenna receiver is large (∼ 4 GHz), the relevant band-width for the smearing effect is only the 2 MHz channelwidth used to image the data.

To empirically test BWS in our data, we selected 106 point-like (0.9 ≤ S t/S p ≤ 1.1) radio sources with SNR>200. Sinceeach source can be observed in up to 11 neighboring pointingswe can compare the peak surface brightnesses obtained in var-ious pointings (S P) relative to the peak surface brightness re-trieved from the mosaic (S M) as a function of distance from thepointing center. If our data were affected by BWS S P/S M wouldexhibit a declining trend with increasing distance from the point-ing center. This surface brightness ratio, obtained by fitting an in-verted parabola at the 106 bright source positions in the individ-ual pointings and the mosaic is shown in the top panel of Fig. 11.The median ratio stays constant (S P/S M ≈ 1) across all distanceranges, with increasing scatter toward higher distances where thenoise is amplified by the primary beam correction. This demon-strates that there are no empirical bandwidth-smearing issues.This is also in accordance with theoretical expectations. A the-oretical prediction for BWS can be made using the Condonet al. (1998) equation [12] for the reduction of peak response

I/I0 ≈ 1/√

1 + 0.46β2 , where β = (∆ν/ν0) × (θ0/θHPBW) equals

fractional bandwidth times offset in synthesized beam-widths.Using the VLA channel width ∆ν = 2 MHz, central frequencyν0 = 3 GHz, distance from the phase center θ0 = 300′′, and beamsize of θHPBW = 0.75′′ the estimated peak reduction amountsto about 2%. The distance was chosen as a minimal distancebetween two different pointing centers. This is illustrated inFig. 12 where we show the peak over total flux density forSNR > 200 sources in different pointings. An offset of ∼ 2.5%is present in this diagram. However, it is not distance depen-dent, and thus unlikely to be related to bandwidth smearing.Thus, for the reasons outlined above, we do not apply any cor-rections for the BWS effect.

3.6. The 3 GHz VLA-COSMOS Large Project catalog

A sample page of the catalog is shown in Table 5. For eachsource we report its ID, the 3 GHz name, the RA and DEC posi-tion (weighted centroid) and error on the position, the total fluxdensity with relative error7, the 3 GHz rms calculated at the po-sition of the source, the SNR of the source, number of pixelsused in flux density integration, the flag for resolved sources,and the flag for multi-component sources. We note that the peaksurface brightness of resolved sources can be obtained by mul-tiplying the SNR with the rms value. The catalog is available inelectronic format in the COSMOS IRSA archive8.

4. Radio spectral indices

Given the wide bandwidth of our VLA-COSMOS 3 GHz surveyand the existence of previous COSMOS radio surveys, we ap-proached radio spectral index calculations in two ways. The firstmethod uses the MSMF algorithm to construct spectral indicesdirectly from our observed data by fitting a two-term Taylorpolynomial to amplitudes between 2 and 4 GHz (MSMF-basedspectral index or αMSMF hereafter). The second method uses thecataloged monochromatic flux densities at 3 GHz in combinationwith the values taken from the 1.4 GHz Joint catalog (Schinnereret al., 2010) to calculate spectral indices between these two fre-quencies (1.4–3 GHz spectral index or α1.4−3 GHz hereafter). InSect. 4.1 we investigate systematics in the MSMF spectral indexmaps, and compare the differently derived spectral indices. InSect. 4.2 we derive the 1.4–3 GHz spectral index distribution forthe full sample of the 3 GHz sources.

4.1. MSMF-based vs. 1.4–3 GHz spectral indices

We can calculate the MSMF-based spectral indices defined foreach source using the wide bandwidth of our observations if thesource has a sufficient SNR between 2 and 4 GHz. This spec-tral index should be viable if SNR>10 for point sources, and upto 10 times higher for diffuse emission (U. Rau, private com-munication). To do so a mosaic of spectral indices (α-map) wasgenerated by dividing the Taylor term 1 (TT1) mosaic by theTaylor term 0 (TT0) mosaic (see Rau & Cornwell, 2011). Foreach source, its spectral index was extracted from the pixel inthe α-map that corresponds to the pixel containing the peak sur-face brightness in the total intensity mosaic.

To investigate possible systematics in the α-map due to wide-band primary beam corrections we utilized the 106 bright, point-

7 We note that the flux errors reported do not depend on the num-ber of pixels used for integration, but scale with the source bright-ness (see Hales et al. 2012, 2014).8 http://irsa.ipac.caltech.edu/frontpage/



0.9

1.0

1.1

0.9

1.0

1.1

SP /

S M

0 2 4 6 8 10Distance (arcmin)

−0.5

0.0

0.5

α P −

α M

a= −0.04 ( 0.01)b= 0.20 ( 0.06)

Fig. 11. Comparison of peak surface brightnesses (top) and MSMF-based spectral indices (bottom) determined inside the mosaic (S M, αM)and individual pointings (S P, αP) as a function of distance from thepointing center for 106 bright, point-like sources (0.9 ≤ S t/S p ≤ 1.1,SNR>200) observed in up-to 11 neighboring pointings at varying dis-tances from the pointing center (gray points). In both panels the largered points and their corresponding errors indicate median values and in-terquartile ranges inside 5 equally spaced distance bins. In the bottompanel these are fit linearly to correct for the trend (see text for details).

Fig. 12. Comparison of peak surface brightnesses over total fluxdensities for 106 bright, point-like sources (0.9 ≤ S t/S p ≤ 1.1,SNR>200) observed in up-to 11 neighboring pointings at varyingdistances from the pointing center (gray points). The large redpoints and their corresponding errors indicate median values andinterquartile ranges inside 5 equally spaced distance bins. The the-oretical prediction of the bandwidth smearing effect is shown by theblue curve (see text for details).

like source sources introduced in Sect. 3.5. For these we derivedMSMF-based spectral indices both in the mosaic and individualpointings. In the bottom panel of Fig. 11 we show the differencebetween such derived spectral indices as a function of distancefrom the pointing center. The MSMF spectral indices show a sys-tematic steepening with increasing distance, which likely arisesdue to an imperfect primary beam correction of TT1.9 To cor-rect for this effect a-posteriori (as necessary here) we performeda linear fit to the trend. We then applied this distance dependentcorrection to each α-map pointing prior to mosaicing to generatean α-mosaic corrected for this effect.

In Fig. 13 we compare the corrected spectral indices fromMSMF with those derived from the cataloged flux densities at

9 We note that the MSMF algorithm is still in active development andthe upcoming software versions should correct for this.

Fig. 13. Comparison between MSMF-based and 1.4–3 GHz derivedspectral indices, where the first were corrected for the observed system-atic trend illustrated in Fig. 11. Red symbols and the corresponding er-rors mark median spectral indices and interquartile ranges, respectively,for sources in different SNR bins (10<SNR<500). The black dashedline marks the median value of the red circles set at 0.02.

3 GHz and 1.4 GHz (Joint catalog, Schinnerer et al. 2010). Thecatalogs were cross-matched using a search radius of 1.3′′ whichis half of the beam size of the lower resolution (1.4 GHz) sur-vey. The sample was further limited to single-component sourceswith SNR> 5 in the 1.4 GHz catalog yielding a total of 2,191sources. Although there are no systematic offsets within the er-ror margins, there is a rather large scatter between the spectralindices obtained with these two methods. A non-negligible frac-tion of this spread is due to the large uncertainty on thein-band (i.e. MSMF derived) spectral indices (a point-likesource with SNR ∼ 50 and α = 0.7 has an uncertainty of∼ 0.1 in its in-band spectral index; Condon 2015). We notethat if the MSMF spectral indices had not been corrected, therewould have been a systematic offset of -0.2 across the entire SNRrange.

In summary, the MSMF-based spectral indices require fur-ther corrections after PB corrections are applied to the data. Dueto this, and the large scatter observed between the MSMF-basedand 1.4–3 GHz spectral indices we do not include the MSMF-based spectral indices in the final catalog. We note that newCASA software versions should intrinsically correct for this. Forthe further analysis of spectral indices presented here we have,therefore, used only the values based on flux density measure-ments at 3 and 1.4 GHz.

4.2. 1.4–3 GHz spectral indices

A significant fraction of 3 GHz sources does not have a coun-terpart in the 1.4 GHz survey because of the better sensitivityof our 3 GHz survey. To properly constrain the distribution ofspectral indices for our 3GHz selected sample without introduc-ing any bias due to neglecting sources not detected in one of thesurveys we employed the survival analysis. This is a statisticalmethod that takes into account both direct detections, as wellas upper (or lower) limits (see Feigelson & Nelson 1985 andSchmitt 1985 for details).

We first cross-correlated and combined our 3 GHz catalogwith the 1.4 GHz Joint catalog (Schinnerer et al., 2010) with amaximum separation of 1.3′′, but also including sources with-out counterparts in one or the other survey. We then removed allsources that fell outside of the area observed at 1.4 GHz as the



area observed at 3 GHz is larger (2.6 square degrees.). This wasdone to ensure the same area for both surveys. 1.4 GHz multi-component sources (80), and their 3 GHz counterparts were alsoremoved. The final sample contains 10,523 entries out of which23% were detected in both surveys, 74% were detected only at3 GHz and 3% were detected only at 1.4 GHz, as illustrated inFig. 14 (top panel). If a source was not cataloged in one of thesurveys we used 5 times the local rms value at the coordinatesof the source as an upper limit on the flux density. Each non-detection at 1.4 GHz yielded one lower limit on spectral index,and similarly, each non-detection at 3 GHz yielded one upperlimit.

A Gaussian fit to the distribution of spectral indices detectedin both surveys (green line in Fig. 14, top panel) results in thepeak at α = −0.84 and a standard deviation of σ = 0.35. As thisresult is valid only for the subsample of 3 GHz sources also de-tected at 1.4 GHz, we employed the survival analysis to accountfor the full 3 GHz detected sample. We therefore ran the survivalanalysis on a single-censored dataset which included only de-tections in both surveys and lower limits. The method assumesthat limits follow the same distribution as direct detections andgenerates a cumulative distribution for all sources in the sam-ple. This is shown in the middle panel of Fig. 14. There wasenough overlap between direct detections and lower limits en-abling the survival analysis to properly constrain the median ofthe total distribution to α = −0.68 ± 0.02, even though therewere three times more limits than detections. This method how-ever cannot constrain all lower limits and the cumulative func-tion does not converge to 0, yielding a total of 6% unconstrainedsources. To constrain these (as needed to derive the probabilitydensity function, PDF, for spectral indices; see below) we em-ployed a physical argument that a radio source exhibiting stan-dard synchrotron self-absorption cannot have a spectral indexhigher than αmax = 2.5 (Rees 1967; unless it is extremely rareand exotic; for example see Krishna et al. 2014). Our data canalso constrain the distribution of spectral indices only up to valueof α = 0.8, since this interval contains 99.5% of sources detectedat both 1.4 and 3 GHz. With these limits we can at best assumea flat probability that unconstrained sources have 0.8 < α < 2.5,and formally extrapolate the cumulative distribution function to0 (red dashed line in Fig. 14, middle panel). Having constrainedthis we then derived the PDF for spectral indices of our 3 GHzsources by calculating the first derivative of the cumulative dis-tribution function extrapolated to 0. The PDF is shown in thebottom panel of Fig. 14. The best-fit Gaussian to the PDF yieldsa mean of α = −0.73 and a standard deviation of σ = 0.35.Both the median of the distribution and the mean of the Gaus-sian fit agree very well with previous work done on spectral in-dices (e.g., Condon 1984; Lisenfeld & Völk 2000; Kimball &Ivezic 2008) and we conclude that our catalog flux densities donot show any significant systematics.

5. Radio source counts corrections

A well established approach to estimate the combined effects ofnoise bias, source extraction and flux determination systematics,inhomogeneuos noise distribution over the imaged field and res-olution bias on the measured source counts (completeness andbias corrections hereafter) is to rely on mock samples of radiosources, as described in Sect. 5.1. As these corrections do nottake into account the fraction of spurious sources (as the mocksources are always inserted into the same mosaic) in Sect. 5.2we separately derive the false detection rate. The combination of

Fig. 14. Top panel: Distribution of 1.4–3 GHz spectral indices forsources detected at both frequencies (green line), and only at 3 GHz(lower limits, blue line) or 1.4 GHz (upper limits, red line). Middlepanel: Cumulative distribution function (CDF, black line) and error es-timate (grey shaded area) of spectral indices calculated using the sur-vival analysis also taking into account lower limits. The red dashed lineshows a linear extrapolation of the distribution to zero assuming themaximum theoretically attainable spectral index of α = 2.5 (see textfor details). Bottom panel: Probability density function (PDF) for spec-tral indices calculated as a first derivative of the CDF extrapolated to0 at high end (middle panel). A Gaussian fit to the distribution is alsoshown (red curve) and its mean and standard deviation are indicated inthe panel.

the two corrections then yields the net radio source count correc-tions.



5.1. Completeness and bias corrections

We here describe the Monte Carlo simulations used to derivethe completeness and bias corrections. Mock sources were in-jected over the imaged field and then recovered using the sametechnique adopted for the real radio sources, as detailed inSect. 5.1.1. The flux density and size distributions assumed aredescribed in Sect. 5.1.2 and Sect. 5.1.3, respectively. The resultsof the final simulations yielding the adopted completeness andbias corrections are detailed in Sect. 5.1.4, and a summary of theeffects taken into account by the completeness and bias correc-tions is given in Sect. 5.1.5.

5.1.1. Retrieval of mock radio sources

The procedure adopted to insert and retrieve mock sources inand from the mosaic is as follows. Since blobcat does not pro-duce a residual map, we inserted mock sources (Gaussian inshape) directly into the continuum map avoiding already cata-loged components. This procedure was limited to the central 2square degrees of the mosaic. For each mock source, a squareshape with a width of 6σ + 21 pixel on the side was requiredto be free of any cataloged emission (real or mock), where σ isthe standard deviation along the Gaussian major axis. The posi-tions were randomly chosen until this was satisfied. At a resolu-tion of 0.75′′ the continuum map is mostly "empty" of sourcesand confusion is negligible. We did not observe any systematicclustering of mock sources toward the less populated parts ofthe mosaic (more noisy parts closer to the edge for example) byrequiring no overlap between the components. After all mocksources were inserted, we ran blobcat with the exact parame-ters as done for the real sources. Since the extraction was doneon a map containing both real and mock emission, all the 10,899real components were always recovered and then removed fromthe extracted catalog, prior to further processing. To generate re-alistic mock catalogs of radio sources we, however, needed toassume i) a flux density distribution in (and below) the rangetested by the observations and ii) an angular size distribution ofthe radio sources. This is described in detail in the following sec-tions.

5.1.2. Flux density distribution

We simulated the flux density distribution using both a simplepower law model (PL model) and a multinode power law (MPLmodel) that better reproduces the observed source counts below500 µJy. In the former case we used the 1.4 GHz source countsfrom previous surveys scaled to 3 GHz (see Bondi et al. 2008).The multinode power law model is that derived by Vernstromet al. (2014) (see their Table 4, Zone 1). For both models themock catalogs were generated down to a total flux density of5 µJy and contained more than 40,000 (65,000) objects in thePL (MPL) model. This allowed us to also count sources with fluxdensities below the SNR threshold as positive noise fluctuationsmight lead these to have a measured peak flux density above oursource detection threshold. As shown below the results of oursimulations do not yield differences between the two models,and we adopted the MPL model for our final simulations.

5.1.3. Angular size distribution

We needed to assign to each mock source an intrinsic angu-lar size. Unfortunately, a satisfying description of the intrinsicsource angular size distribution at sub-mJy flux density is still

missing and we needed to rely on extrapolations from higherflux densities. Bondi et al. (2008) used a simple power lawparametrization distribution of the sources’ angular sizes as afunction of their total flux density. We followed the same methodwith some adaptations, as described below.

The angular size (θ) distribution was simulated assuminga power law relation between angular size and flux density(θ ∝ S n). This relation was normalized using the cumulativeangular size distribution derived at ∼ 1 mJy from the VVDS 1.4GHz observations with a resolution of 6′′ (Bondi et al., 2003).The relatively low resolution of the VVDS survey allowed usnot to be biased, in our simulations, against sources with an-gular sizes of up to 15′′ (Bondi et al., 2003). We explored therange of n values between 0.3 and 1.0 in steps of 0.1. To in-fer the best n value, the angular size distribution of the sourcesfrom the catalog in a specific total flux density range was com-pared with the corresponding distribution derived from the mocksamples with different n values. The value of n which gave thebest match between the angular size distribution of observed andmock sources was then chosen as the best approximation for theintrinsic source size versus total flux density relation.

Since the observed source angular sizes are not provided byblobcat, these were estimated using the relation between theratio of the total flux densitiy and peak surface brightness andangular sizes:

S t

S p

=

√

θ2M+ θ2

b

√

θ2m + θ2b

θ2b

(1)

where S t is the total flux density, S p is the peak surfacebrightness, θb is the FWHM of the circular beam (0.75′′ in ourobservations), θM and θm are the major and minor FWHM in-trinic (deconvolved) angular sizes (see Bondi et al. 2008 wherethe same approach was used to derive a size estimate of sourcesaffected by bandwidth smearing). In doing so we needed to makesome assumptions on the morphology of the sources and in par-ticular on how the sources are, eventually, resolved. We consid-ered two limiting cases:

1. Elongated geometry: Sources are resolved in only one direc-tion. This implies that θm = 0 and

S t

S p

=

√

θ2M+ θ2

b

θ2b

(2)

The simulated mock sources were accordingly generated assources extended in one direction and eq. 2 is the appropriaterelation between S t/S p and the angular size.

2. Circular geometry: Sources are uniformly resolved in all di-rections. This implies that θM = θm and

S t

S p

=θ2

M+ θ2

b

θ2b

(3)

The simulated mock sources were accordingly generated assources uniformly extended in all directions and eq. 3 is theappropriate relation between S t/S p and the angular size.

Mock catalogs were generated for each combination of the2 source count models (PL and MPL), the 8 different n values(0.3–1.0 in steps of 0.1), and the 2 different source geometries



(θm = 0 or θm = θM). For each of these 32 combinations wegenerated and merged 10 different mock samples. Then, we de-rived for each of the 32 different mock catalogs the S t/S p dis-tributions for sources with S t < 100 µJy, splitting them into twosub-ranges: S t ≤ 40 µJy, and 40 < S t ≤ 100 µJy. This range intotal flux density is the one more affected by the choice on theintrinsic source size distribution and therefore is the best suitedfor a comparison between the S t/S p distribution of the real cat-alogued sources and that derived from the mock samples repro-cessed as the observed catalog. Using S t/S p as a proxy for theangular size of the radio sources has the advantage that we donot need to deal with upper limits in the measured source sizesbecause of sources classified as unresolved.

The results of this comparison can be summarized as follows.No significant differences were found using the PL or MPL dis-tributions for the source counts. For this reason, we could adopteither of the two models in the following analysis and we de-cided to use the MPL model which provides a more realisticand detailed description of the observed source counts. How-ever, none of the 16 combinations of n value and source geome-try provided a satisfying match between the S t/S p distribution ofthe reprocessed mock catalog and that of the observed catalog,in the flux density range S t < 100 µJy. While some combina-tions of parameters provided a reasonable match for sources withS t & 40 µJy, they all failed to reproduce the observed distribu-tion of S t/S p below this threshold. In particular, the mock sam-ples showed lower values of S t/S p than the catalog for S t . 40µJy. This is shown in Fig. 15 where we plot in the two panels theS t/S p distribution for sources with S t < 40 µJy and sources with40 < S t ≤ 100 µJy, respectively. Together with the observed dis-tribution derived from the sources in the catalog we plot also thedistribution obtained from our original simulation using n = 0.6and elongated geometry. The two distributions are clearly shiftedand this effect is found in all the simulations.

This result is not completely unexpected, The extrapolationto very low flux density of our power law relation between angu-lar size and flux density (which has been previously tested onlyfor sources more than one order of magnitude brighter) producesmock samples of radio sources dominated by extremely compactobjects at the faint end of the total flux density distribution. Forinstance, for the simulations shown in Fig. 15 45% of all thesources with S t ≤ 40 µJy have S t/S p < 1. This result is at oddswith the distribution of the observed catalog, where only 26% ofthe observed sources fainter than 40 µJy have S t/S p < 1.

The simplest way to decrease the number of extremely com-pact objects at the faint end of the flux distribution in our mocksources, without modifying the adopted power law relation be-tween angular size and flux density, is to apply a minimum an-gular size to the faint mock sources. We tested the followingexpression for θmin:

θmin = k1e−(S t/k2)2(4)

in which the exponential part is motivated by the fact that, onthe basis of the analysis shown in the lower panel of Fig. 15, noθmin is required at flux densities & 40 microJy. We included theminimum angular size requirement in our procedure to generatethe mock samples of radio sources and repeated the simulations,the extraction process and the comparison of the S t/S p distri-butions. By varying the parameters k1 and k2 we found that thebest value for the k2 parameter is k2 = 40 µJy while for the nor-malization factor k1 is equal to 0.3 (for the elongated geometry)and 0.2 (for the circular geometry). The different normalizationis necessary because for a given intrinsic source size the area

covered by a circular source is larger, and derived from eq. 2and 3. As shown in Fig. 15, this time we found a very goodagreement between the observed and simulated distributions ofS t/S p also at low flux densities, In particular, for the simula-tion shown in Fig. 15, introducing a minimum angular size asa function of the total flux density reduces the fraction of faintsources (S t ≤ 40 µJy) with S t/S p < 1 from 45% to 30% close tothe observed value of 26%. Thus, for our final simulations usedto derive the completeness and bias corrections we adopted theabove described size parametrization.

We further found that the geometry of the radio sources hassome effects on the results we obtain. For elongated geometry(θm = 0) we obtained the best match between the S t/S p distri-butions for n = 0.5 − 0.6, for circular geometry (θm = θM) thebest match was obtained for n = 0.6− 0.7. We note that both theassumptions made on the source geometry are clearly simplisticand real sources will consist of a mix of elongated and circularsources. Thus, to compute our final completeness and bias cor-rections for the adopted MPL flux density distribution modelswe computed the completeness and bias correction factors us-ing the average of those from the 4 best-matched simulations –i) elongated sources with n = 0.5, and n = 0.6, and ii) circularsources with n = 0.6, and n = 0.7, as described in more detail inthe next section.

5.1.4. Derivation of completeness and bias corrections

We generated 60 mock catalogs using the parameterization asdescribed above (Sect. 5.1.2 and Sect. 5.1.3; see also below).The mock sources were inserted into the mosaic and retrieved asdescribed in Sect. 5.1.1. The retrieved mock sources were thencross-correlated with the input mock catalog and their measuredtotal flux density chosen to be either their integrated flux densityif resolved, or peak surface brightness if unresolved. For this, thesame S t/S p envelope was used as described in Sect. 3. Lastly,successfully extracted mock sources and original mock sourceswere binned separately in flux densities. The ratio of their num-bers in each flux density bin represents the completeness andbias correction factor.

In Fig. 16 we show the net result of the above describedMonte Carlo simulations for the MPL model and best-matchedsimulations, i.e. i) elongated sources with n = 0.5 and 0.6, andii) circular sources with n = 0.6 and 0.7. We take the average ofthese simulations as the completeness and bias correction, with aconfidence interval that takes into account the differences withinthe 6 sets of simulations. This is tabulated in Table 2. For refer-ence, in Fig. 16 we also show the average completeness and biascorrections obtained using only the elongated and circular geom-etry approximations. The net curve yields values of about 55% at12 µJy (SNR=5.2), and rather constant up to 20 µJy (SNR <9),beyond which they rise to a 94% completeness above 40 µJy(SNR≥16). The mean error of the completeness and bias cor-rections is 5%. The two (elongated and circular geometry) ap-proximations are consistent up to ∼ 30 µJy, beyond which theystart diverging with the circular approximation being systemati-cally lower at higher flux densities. However, beyond this limitboth curves saturate at fairly constant values (∼ 0.92 for circularand 0.98 for elongated morphology), implying average values ofover 95% for fluxes higher than ∼ 40 µJy.



catalog 10 MPL, n=0.60, long

0 0.5 1 1.5 20

0.05

0.1

catalog 10 MPL, n=0.60, long

0 0.5 1 1.5 20

0.05

0.1

Fig. 15. Total-to-peak flux density ratio distributions in two total fluxdensity ranges: S t ≤ 40 µJy (top panel) and 40 < S t ≤ 100 µJy (bot-tom panel). Each panel shows the distribution of the observed sources(red histogram), that derived from the 10 sets of simulations using anelongated geometry and n = 0.6, no minimum angular size (green his-togram) and with a minimum angular size θmin = 0.3e−(S t/40)2

(blue his-togram).

5.1.5. Biases addressed

There are several effects and biases that occur in the catalogingprocess which we addressed through our simulations. Firstly, anincompleteness in the extracted catalog will exist as real sourceson the sky will not be detected if i) their peak surface brightnessfalls below the chosen threshold of 5σ because of fluctuationsin the local rms, ii) they are extended enough for their peak sur-face brightness to fall below the detection threshold, even thoughtheir integrated flux density is well above it. Secondly, a contam-ination effect will also be present. If a source is detected, its fluxdensity might be wrongly computed due to the presence of anoise peak. Statistically, this effect is mostly symmetric aroundthe mean flux density. However, when we set the total flux den-

Fig. 16. Completeness of our 3 GHz source catalog as a function offlux density and SNR. The mean completeness of all Monte Carlo runs(red line) and its standard deviation (grey shaded area) are shown. Alsoshown are the corrections when elongated (dash-dotted line) and circu-lar (dashed line) geometries are assumed.

Table 2. Completeness and bias correction factors for the VLA-COSMOS 3 GHz catalog as a function of flux density

Flux density Completeness and bias Error(µJy) correction factor (Ccompl)< 10.4 0 -11.0 0.08 0.0111.6 0.40 0.0212.3 0.55 0.0313.0 0.58 0.0313.8 0.56 0.0414.6 0.57 0.0315.5 0.57 0.0416.4 0.57 0.0417.3 0.57 0.0418.4 0.59 0.0419.4 0.56 0.0421.1 0.68 0.0523.3 0.73 0.0425.8 0.82 0.0528.6 0.85 0.0531.7 0.89 0.0635.1 0.91 0.0738.8 0.94 0.0643.0 0.92 0.0647.6 0.95 0.0753.9 0.94 0.0562.4 0.95 0.0772.2 0.93 0.0683.5 0.92 0.0896.7 0.97 0.08> 100a 1.00a 0.05a

aAssumed corrections for fluxes > 100 µJy.

sity of an unresolved source to its peak surface brightness wemay introduce an asymmetric bias toward smaller flux densities.Some sources with S t > S p within the envelope in Fig. 9 mighttruly be resolved, however noise variations do not allow to de-termine this with sufficiently high accuracy leading to a potentialbias. The final result is that a source can jump into a flux densitybin where it does not belong, thus increasing its contamination.The combination of completeness, which always decreases with



decreasing flux density, and the significant number of sourcesthat move from their original flux density bin to another due toerrors in flux measurement at faint flux densities, produces theflat distribution of the completeness and bias correction factorseen at flux densitites of ∼ 12 − 20 µJy in Fig. 16.

In summary, the simulations we performed account for boththe fraction of non-detected sources (incompleteness), and alsothe redistribution of sources between various flux density bins.Thus, in principle, its value can be larger than one if the con-tamination is high. These corrections, however, do not take intoaccount the fraction of spurious sources as a function of fluxdensity, which are separately derived in the next section.

5.2. False detection rate

To assess the false detection rate of our source extraction we ranblobcat on the inverted (i.e., multiplied by −1) continuum mapwith the same settings used for the main catalog. Since thereis no negative emission on the sky, every source detected inthe inverted map is per-definition a noise peak (i.e. a false de-tection). The source extraction returned 414 negative detectionswith SNR ≥ 5 across the entire observed field, 95 of which wereoutside the central 2 square degrees, demonstrating that 23% offalse detections lies at the edge of the mosaic.

The highest SNR negative detections were predominantly lo-cated around true bright sources as they suffer from artifacts (upto six negative components could be found around a single brightobject due to the VLA synthesized beam shape; see also Sect.7.1.1. in Vernstrom et al. 2014 for an explanation of this effect).Since extraction of real emission does not exhibit this behaviorwe removed all negative components that were less than 3′′ awayfrom a real source with SNR> 100. This step removed further40 components. We additionally removed 4 sources with catas-trophic peak estimates which increased their SNR by more thana factor of four due to poor parabola fits (we note that there wereno such sources in the catalog of real emission). The remaining275 negative detections within the inner 2 square degrees werethen classified into resolved and unresolved using the same en-velope as was done for the real data. Finally, they were binned inSNR and flux densities alongside true detections to enable directcomparison. The results are shown in Fig 17 and also listed inTable 3. As expected, only the lowest SNR bins have a notice-able fraction of false detections (24% for SNR= 5.0–5.1) whichquickly decreases to less than 3% for any SNR bin at SNR> 5.5.The estimated fraction of spurious sources over the entire cata-log above SNR> 5 (5.5) drawn from the inner 2 square degreesis only 2.7 (0.4)% .

6. Radio source counts

In this section we present our 3 GHz radio source counts(Sect. 6.1), and compare them to 3 GHz and 1.4 GHz countsavailable in the literature (Sects. 6.2 and 6.3, respectively).

6.1. VLA-COSMOS 3 GHz radio source counts

We present our 3 GHz radio source counts normalized to Eu-clidean geometry, both corrected and uncorrected, in the toppanel of Fig. 18. In Table 4 we list the counts, errors, the numberof sources and the radio source count corrections (i.e., complete-ness and bias and false detection fraction corrections) in eachflux density bin. The source count errors take into account boththe Poissonian errors as well as completeness and bias correc-

Fig. 17. Fraction of false detections (red line) as a function of SNR(top panel) and flux density (bottom panel). The open (filled) histogramshows the number of components cataloged in the observed 3 GHz mo-saic (detected in the inverted map), and limited to the central 2 squaredegrees. The data is also listed in Table 3.

tion uncertainties. We note that most of our sources are located atlow flux densities (below 0.5 mJy), with more than 500 sourcesin each flux density bin below 60 µJy resulting in small Poisso-nian errors. As evident from the plot, our source counts at 3 GHzexhibit a flattening at about 0.3 mJy that continues one order ofmagnitude in flux densities down to 30 µJy, steepening further atfainter flux densities.

6.2. Comparison with 3 GHz counts from the literature

In the middle panel of Fig. 18 we compare our 3 GHz sourcecounts with other 3 GHz counts available in the literature (Con-don et al., 2012; Vernstrom et al., 2014). Condon et al. (2012)performed a P(D) analysis using 3 GHz confusion-limited databased on 50-hours of on-source C-configuration observations ofone VLA pointing targeting the Lockman hole and reaching anrms of 1 µJy beam−1. Fitting single-power law models to thedata the analysis allowed them to constrain the counts of discretesources in the 1−10 µJy range, also shown in Fig. 18 . Vernstromet al. (2014) performed a more complex P(D) analysis on thesame data fitting various (modified power-law, and node-based)models to the data allowing to probe the counts down to 0.1 µJy.In Fig. 18 we show the counts based on the fit of a phenomeno-logical parametric model of multiple joined power laws (theirnode-based model) applied to the inner circular area with a 5′

radius (their Zone 1; see Vernstrom et al. 2014 for details).The counts derived here are in very good agreement with

those derived by Condon et al. (2012). Fitting the five faintestflux density bins using a power-law, dN/dS ∝ S γ, we find that



Table 3. False detection probability as a function of SNR and flux den-sity in the COSMOS 2 square degree field

SNR Fraction

5.05 0.245.15 0.155.25 0.115.35 0.095.45 0.065.55 0.035.65 0.025.75 0.035.85 0.015.95 0.026.05 0.016.15 0.016.25 0.026.35 0.016.45 0.006.55 0.006.65 0.016.75 0.016.85 0.006.95 0.01

Flux density Fraction(µJy) (Ffalse−det)10.75 0.4011.00 0.3811.25 0.2711.50 0.2111.75 0.1512.00 0.1312.25 0.0912.50 0.0712.75 0.0613.00 0.0613.25 0.0313.50 0.0413.75 0.0314.00 0.0514.25 0.0314.50 0.0314.75 0.0815.00 0.0815.25 0.0015.50 0.01

the slope γ = −1.72 is perfectly consistent with that inferred byCondon et al. (2012), while our normalization is slightly lower.Our comparison to the Vernstrom et al. (2014) results shows thatthe counts are in agreement down to ∼ 30 µJy with a discrepancyat fainter flux densitites as our counts are systematically lowerthan theirs.

In general, the strength of the P(D) analysis is the ability toprobe counts below the nominal noise in the data, while avoid-ing resolution biases as it is applied on confusion-limited (thus,low resolution) data. However, as the P(D) analyses discussedabove were performed on a single VLA pointing the resultingcounts may be subject to cosmic variance due to the small areacovered. This could potentially explain the observed discrepancybetween the VLA-COSMOS 3 GHz Large Project counts basedon a 2 square degree area and the Vernstrom et al. (2014) re-sults based on a 0.022 square degree area (their Zone 1). Totest this we subdivided the 2 square degree COSMOS field into100 square and non-overlapping subfields, each with an area of0.020 deg2 roughly corresponding to a circle with a radius of5′. In the middle panel of Fig. 18 we show the range of suchobtained counts (corrected for completeness and bias, and falsedetection fractions, calculated on the full 2 square degrees anddescribed in Sect. 5). We find that sample variance, quanti-fied in this way, can introduce a (1σ) scatter of +0.1

−0.2 dex in thesource counts. We note that the distribution in counts in the100 subfields are likely to be an under-estimate of the truecosmic variance (dominated by cosmic large-scale structure,rather than sample variance), because these fields are likelynot fully independent from each other. Thus, cosmic variancemay explain the observed discrepancy.

6.3. Comparison with 1.4 GHz counts from the literature

To compare our result with more abundant 1.4 GHz observationsand models (e.g. Condon 1984; Bondi et al. 2008; Owen & Mor-rison 2008; Wilman et al. 2008; Condon et al. 2012, see also de

Fig. 18. Top panel: VLA-COSMOS 3 GHz Euclidean-normalized ra-dio source counts, corrected using the completeness and bias and false-detection correction factors (black filled points) and without correc-tions (gray squares). Middle panel: VLA-COSMOS 3 GHz radio sourcecounts compared to Condon et al. (2012) P(D) analysis with a singlepower-law (dot-dashed red line) and Vernstrom et al. (2014) P(D) anal-ysis with multiple power-laws (green line) at 3 GHz. The yellow shadedarea contains 95% of different source counts obtained from 100 squareand non-overlapping (8.5×8.5 arcmin2) subfields of the COSMOS field,thus demonstrating the effect of cosmic variance on fields with sizessimilar to those analyzed by Condon et al. (2012) and Vernstrom etal. (2014). The dashed orange line shows the 68% interval of differentsource counts (obtained from 16th and 84th percentile in each flux den-sity bin). Bottom panel: Counts of the same sources, but shifted to the1.4 GHz observed frame using a spectral index of α = −0.7 prior to bin-ning (black filled points). A selection of existing 1.4 GHz source countsin the literature is also shown, as indicated in the legend.

Zotti et al. 2010) we scale our flux densities to the 1.4 GHz ob-served frame using a spectral index of -0.7. This value, also inagreement with the spectral index survival analysis described in



Table 4. Radio source counts at 3 GHz within the COSMOS 2 squaredegree field, normalized to Euclidean geometry

Flux density Countsa Errorb N Correction(mJy) (Jy1.5sr−1) (Jy1.5sr−1) factora

0.011 0.866 0.068 631 3.270.013 0.952 0.056 1109 1.640.015 1.10 0.078 991 1.700.018 1.16 0.094 849 1.670.020 1.40 0.11 888 1.540.024 1.38 0.086 811 1.330.028 1.47 0.10 780 1.180.032 1.57 0.12 702 1.120.037 1.59 0.13 587 1.080.045 1.58 0.13 753 1.070.059 1.53 0.12 505 1.050.076 1.67 0.14 366 1.080.098 1.60 0.17 250 1.030.13 1.65 0.15 181 1.000.16 1.62 0.17 121 1.000.21 1.82 0.21 93 1.000.27 1.93 0.25 67 1.000.35 2.03 0.31 48 1.000.78 3.95 0.37 159 1.003.0 10.4 1.5 56 1.0011 37.4 7.4 27 1.0044 72.3 28 7 1.00

a The listed counts were corrected for completeness and bias(Ccompl), as well as false detection fractions (Ffalse−det) bymultiplying the raw counts by the correction factor given in thelast column, and equal to (1-Ffalse−det)/Ccompl (see Table 2 andTable 3).b The source count errors take into account only thePoissonian errors and completeness and bias correctionuncertainties (see text for details).

Sect. 4, is commonly used and provides the easiest comparison(e.g., Condon et al. 2012). We show the 1.4 GHz source countcomparison in the bottom panel of Fig. 18.

The large spread of the 1.4 GHz source counts available inthe literature at submillijansky levels (see e.g., Fig. 1 in Smolcicet al. 2015) is usually attributed to a combination of i) cosmicvariance as often the observed fields are rather small (see Fig. 1and middle panel of Fig. 18) and ii) resolution bias leading toa loss of sources in radio continuum surveys conducted at in-termediate to high (. 2′′) angular resolution (as described inmore detail in Sect. 5.1.5). The large, 2 square degree area of theCOSMOS field minimizes the effect of cosmic variance, and inSect. 5 we have performed extensive Monte Carlo simulations toaccount for potential resolution biases. Our source counts agreewell with those derived by Condon et al. (2012) based on theP(D) analysis at the faint end (see previous section).

The counts derived here are in good agreement with thosederived from the VLA-COSMOS 1.4 GHz Large Project (Schin-nerer et al. 2007; Bondi et al. 2008; red diamonds in Fig. 18) atflux densities higher than ∼ 200 µJy, while the latter are higherin the flux density range of 100 − 200 µJy. As this is the samefield cosmic variance cannot explain the discrepancy. We notethat the uncorrected counts from the two surveys are in verygood agreement, and that the difference is the largest in the fluxdensity range where the 1.4 GHz survey is the least complete

(about 60%), and the corrections, thus, the largest. In the sameflux density range the corrections for the 3 GHz survey are notas severe given the much higher sensitivity of the 3 GHz sur-vey. Further reasons that could explain part of the discrepancyare i) the effect of bandwidth smearing on the radio source countcorrections, present in the 1.4 GHz data, but not in the 3 GHzdata (see Bondi et al. 2008) and ii) a possibly overly simplisticscaling of the 3 GHz counts to 1.4 GHz using just one spectralindex value. Source counts at 1.4 GHz depend on the steepnessof the counts at 3 GHz and the spread of the spectral indices. Weleave the analysis of the potential bias in source counts due tothis effect to an upcoming paper (Novak et al., in prep.).

The largest discrepancy between the counts derived here andthose in the literature is observed relative to the Owen & Mor-rison (2008) results. Owen & Morrison (2008) have observedthe Lockman hole at 1.4 GHz in A, B, C, and D configurationswith the VLA reaching an angular resolution of ∼ 1.6′′ andrms ≈ 2.7 µJy beam−1. To correct for the resolution bias theyhave assumed a source size distribution with an extended tail atthe high end (see their Fig. 8), and that remains constant as afunction of flux density. The source count corrections are signif-icant under these assumptions and result in a flat source countdistribution at flux densities fainter than ∼ 200 µJy (green pointsin the bottom panel of Fig. 18). As already discussed by Con-don et al. (2012) and Vernstrom et al. (2014) these correctionsare most likely overestimated. In contrast, for the correctionsapplied to the data presented here we have assumed a modelfor radio source sizes such that the radio size is a function offlux density, with a limiting minimum size (see Sect. 5.1). Theagreement between our source counts and those derived fromconfusion-limited data (Condon et al., 2012; Vernstrom et al.,2014) further strengthens the validity of this assumption.

In Fig. 18 we also compare our results with the models de-veloped by Condon (1984), Wilman et al. (2008), and Bétherminet al. (2012). The faint end of our counts (. 80 µJy), combinedwith the results from Condon et al. (2012) which appear as anextrapolation of our data, agree the best with the Condon (1984)model. The model was constrained by source counts, redshift,and spectral-index distributions for various 400 MHz to 5 GHzflux limited samples, as well as the local 1.4 GHz luminosityfunction for two dominant, spiral and elliptical galaxy popula-tions. The adopted model is not a unique solution, and evolvesall sources (ellipticals and spirals, steep- and flat-spectrum) inthe same way. At flux densities above ∼ 80 µJy the Condon(1984) model is slightly higher than our derived source counts,and consistent with the counts determined by Vernstrom et al.(2014).

Our derived source counts deviate from those predicted bythe Wilman et al. (2008) and Béthermin et al. (2012) models.While they agree with the first down to ∼ 100 µJy, they are sys-tematically higher at fainter flux densities. On the other hand,the Béthermin et al. (2012) model underpredicts our counts inthe flux density range of ∼ 50 − 300 µJy, while it overpredictsthe counts at flux densities . 30 µJy. The discrepancies maypossibly be understood when considering how the AGN and starforming galaxies were implemented in the models. Bétherminet al. (2012) implement only models for X-ray selected AGN(L2−10 keV ∼ 1042 − 1044 erg s−1; see Mullaney et al. 2011, 2012;Aird et al. 2012), and thus ignore the population of radio-loudAGN hosted by red, quiescent galaxies, regularly not identi-fied as X-ray AGN, yet still substantial (e.g., Best et al., 2006;Smolcic et al., 2008b; Bonzini et al., 2013; Baran et al., 2016;Delvecchio et al., 2016). This could explain the lack of sourceswith flux densities in the range of ∼ 50 − 300 µJy in the model



(see e.g., Smolcic et al., 2008b; Padovani et al., 2015; Baranet al., 2016), compared to the observational results. On the otherhand, as Béthermin et al. (2012) model the star forming galaxypopulation tracing the star-forming galaxy main sequence, andthe stellar mass function over cosmic time, and taking main-sequence and starburst galaxy spectral energy distribution li-braries into account, using the most recent results (Bouwenset al., 2007; Rodighiero et al., 2011; Magnelli et al., 2011; Karimet al., 2011; Sargent et al., 2012), the excess of this model com-pared to that of Wilman et al. (2008) could suggest that the lattercarries potential for improvement in modeling the star forminggalaxy population.

7. Summary and conclusions

We presented the VLA-COSMOS 3 GHz Large Project based on384 hours of observations with the Karl G. Jansky Very LargeArray at 3 GHz (10 cm) toward the 2 square degree COSMOSfield. Our final mosaic, imaged per pointing with the multi-scalemulti-frequency algorithm and self-calibration, reaches a me-dian rms of 2.3 µJy beam−1 over the 2 square degrees, at anangular resolution of 0.75′′. We further presented a catalog of10,830 radio sources. Combining our data with the 1.4 GHzVLA-COSMOS Joint Project data using survival analysis wefound the expected median spectral index α of -0.7. Comparingthe positions of our 3 GHz sources with those from the high-resolution VLBA imaging at 1.4 GHz, we estimated that theastrometry is accurate to 0.01′′ at the bright end. Radio sourcecount corrections were calculated for the central 2 square de-grees and used to infer radio source counts. The radio angularsize parametrization adopted based on the comparison of mockversus real source total over peak flux density ratios suggeststhat the angular sizes of radio sources at these flux density levelscan be modeled as a power-law in flux density (θ ∝ S n) with aminimal, flux-dependent size cut-off (eq. 4). Our corrected ra-dio counts with direct detections down to 20 µJy (at 1.4 GHz)are consistent with those derived based on P(D) analyses (Con-don et al., 2012), and agree best with the Condon (1984) model,while they are systematically higher than those predicted by theSKADS (Square Kilometer Array Design Studies) simulations(Wilman et al., 2008).

The VLA-COSMOS 3 GHz Large Project provides to-datesimultaneously the largest and deepest radio continuum survey,bridging the gap between radio continuum surveys conductedwith past generation and those planned with the next generationfacilities. These radio data, in conjunction with the vast panchro-matic COSMOS datasets, will allow for the exploration of var-ious cosmologically relevant topics, such as i) the characteris-tics of the microJansky radio population, ii) radio-quiet QSOsby direct detection in the radio band, iii) modes of star forma-tion at early cosmic epochs, and iv) studying stellar mass growthin typical galaxies since early cosmic epochs and star formationquenching via AGN feedback.

Acknowledgements. Based on observations with the National Radio AstronomyObservatory which is a facility of the National Science Foundation operated un-der cooperative agreement by Associated Universities, Inc. This research wasfunded by the European Union’s Seventh Frame-work programs under grantagreements 333654 (CIG, ’AGN feedback’) and 337595 (ERC Starting Grant,’CoSMass’). MB and PC acknowlege support from the PRIN-INAF 2014. AKand FB acknowledge support by the Collaborative Research Council 956, sub-project A1, funded by the Deutsche Forschungsgemeinschaft (DFG). BM andFB acknowledge support through DFG priority program 1573 founded by theDFG.

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ID NAME RA RA_ERR DEC DEC_ERR FLUX FLUX_ERR RMS SNR NPIX RES MULTI(J2000, deg) (arcsec) (J2000, deg) (arcsec) (µJy) (µJy) (µJy beam−1)

78 COSMOSVLA3 J095709.33+020940.7 149.288886 0.01 2.161331 0.01 13400.0 670.0 28.7 385.0 104 1 01110 COSMOSVLA3 J095709.83+015457.4 149.290996 0.021 1.915946 0.021 1190.0 64.0 22.1 29.0 102 1 05144 COSMOSVLA3 J095710.49+013644.7 149.29372 0.065 1.612418 0.065 145.0 19.0 17.4 8.32 20 0 03749 COSMOSVLA3 J095710.53+025132.2 149.29389 0.053 2.858966 0.053 345.0 32.0 26.8 10.4 31 1 010099 COSMOSVLA3 J095710.57+022657.0 149.294072 0.1 2.449174 0.1 92.0 18.0 17.4 5.3 11 0 04979 COSMOSVLA3 J095710.88+020929.8 149.295339 0.076 2.158297 0.076 2820.0 140.0 21.4 7.13 332 1 03366 COSMOSVLA3 J095711.09+023031.3 149.296231 0.048 2.508722 0.048 318.0 27.0 21.5 11.4 35 1 08753 COSMOSVLA3 J095711.15+021104.2 149.296459 0.095 2.184514 0.095 121.0 22.0 21.2 5.68 18 0 04046 COSMOSVLA3 J095711.64+021236.8 149.298529 0.055 2.210248 0.055 223.0 26.0 22.6 9.83 22 0 06546 COSMOSVLA3 J095711.67+021401.3 149.298655 0.077 2.233706 0.077 135.0 21.0 19.3 7.02 18 0 0

...10942 COSMOSVLA3 J100034.76+014635.7 150.144846 -99.0 1.776607 -99.0 374.0 -99.0 2.4 -99.0 828 1 19229 COSMOSVLA3 J100034.78+025027.4 150.144947 0.1 2.840947 0.1 25.6 2.7 2.4 5.18 25 1 08777 COSMOSVLA3 J100034.80+021421.1 150.145009 0.095 2.239195 0.095 13.0 2.4 2.27 5.7 14 0 0489 COSMOSVLA3 J100034.81+025515.6 150.145042 0.013 2.921023 0.013 229.0 13.0 3.66 62.5 49 0 0439 COSMOSVLA3 J100034.83+014247.1 150.145157 0.013 1.713091 0.013 162.0 9.0 2.27 71.3 51 0 0

2850 COSMOSVLA3 J100034.94+020234.9 150.145599 0.042 2.043054 0.042 29.9 2.8 2.29 13.1 29 0 02439 COSMOSVLA3 J100034.99+024524.5 150.145815 0.038 2.756821 0.038 32.7 2.8 2.22 14.7 29 0 02837 COSMOSVLA3 J100035.00+024614.3 150.145836 0.041 2.770643 0.041 39.6 2.9 2.18 13.3 41 1 04092 COSMOSVLA3 J100035.05+024154.6 150.146065 0.055 2.69852 0.055 28.3 2.6 2.23 9.93 31 1 04148 COSMOSVLA3 J100035.07+020350.5 150.14614 0.057 2.064044 0.057 23.4 2.7 2.43 9.64 23 0 0

...5351 COSMOSVLA3 J100345.81+015420.5 150.940886 0.067 1.905719 0.067 117.0 16.0 14.6 8.05 18 0 05225 COSMOSVLA3 J100346.48+023458.3 150.943703 0.067 2.582882 0.067 127.0 17.0 15.5 8.14 21 0 08447 COSMOSVLA3 J100346.52+022031.2 150.943867 0.11 2.342001 0.11 290.0 20.0 14.4 5.04 48 1 010677 COSMOSVLA3 J100346.56+015500.1 150.944027 0.11 1.916707 0.11 75.7 15.0 14.9 5.1 11 0 06533 COSMOSVLA3 J100346.63+022415.8 150.944306 0.076 2.404402 0.076 143.0 16.0 14.2 7.09 28 1 02195 COSMOSVLA3 J100347.12+022510.6 150.946345 0.036 2.419631 0.036 548.0 31.0 15.3 15.6 83 1 010084 COSMOSVLA3 J100347.27+020117.6 150.94699 0.1 2.021575 0.1 73.1 15.0 14.1 5.18 16 0 09695 COSMOSVLA3 J100347.51+023539.7 150.947979 0.1 2.594384 0.1 93.2 18.0 17.6 5.3 10 0 010652 COSMOSVLA3 J100347.80+024951.9 150.949175 0.11 2.831096 0.11 80.7 17.0 16.1 5.01 14 0 010484 COSMOSVLA3 J100348.53+021102.3 150.952242 0.11 2.183987 0.11 82.3 17.0 16.3 5.05 13 0 0

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The VLA-COSMOS 3 GHz Large Project: Continuum data ...vs/papers_dr1/Smolcic_et_al_data.pdf3 NAF-Osservatorio Astronomico di Bologna, Via Ranzani 1, I - 40127 Bologna, Italy 4 California